标题： 射影结构 on 一个黎曼曲面 显示英文标题

标题： Projective structures on a Riemann surface

摘要： For a compact Riemann surface $X$ of any genus $g$, let $L$denote the line bundle $K_{X\times X}\otimes {\cal O}_{X\times X}(2\Delta)$ on $X\times X$, where $K_{X\times X}$ is the canonical bundle of $X\times X$ and $\Delta$ is the diagonal divisor. 我们证明$L$在非约化除子$2\Delta$上有一个规范的平凡化。 我们的主要结果是，$X$上的射影结构空间与所有在$3\Delta$上的$L$的平凡化空间之间存在规范的对应关系，这些平凡化限制到上述提到的$L$在$2\Delta$上的规范平凡化。 我们直接地将这种射影结构的定义与 Deligne 的定义进行了对应。 我们还简要描述了这项工作的来源，即在共形量子场论中所谓的“能量-动量张量的 Sugawara 形式”的研究中。 显示英文摘要

摘要： For a compact Riemann surface $X$ of any genus $g$, let $L$denote the line bundle $K_{X\times X}\otimes {\cal O}_{X\times X}(2\Delta)$ on $X\times X$, where $K_{X\times X}$ is the canonical bundle of $X\times X$ and $\Delta$ is the diagonal divisor. We show that $L$ has a canonical trivialisation over the nonreduced divisor $2\Delta$. Our main result is that the space of projective structures on $X$ is canonically identified with the space of all trivialisations of $L$ over $3\Delta$ which restrict to the canonical trivialisation of $L$ over $2\Delta$ mentioned above. We give a direct identification of this definition of a projective structure with a definition of Deligne.We also describe briefly the origin of this work in the study of the so-called "Sugawara form" of the energy-momentum tensor in a conformal quantum field theory.